At least 70 people have been killed in Bangladesh after heavy rains flooded the south-east port city of Chittagong and set off landslides in surrounding areas.

A further seven people were struck by lightning in two northern and western districts.

Chittagong police and city council officials said the landslides had buried dozens of homes in hilly districts around the city of five million, and warned the death toll could still rise.

Chittagong police chief Moinur Rahman Chowdhury says the situation is "very grave" and it is still raining hard in the city.

Local government chief Mukhlesur Rahman says so far 70 bodies have been recovered in the port city.

He has warned the death toll could rise further as "reports of casualties are coming in every hour".

Most of the victims were killed by landslides.

Police and city council officials say the landslides have buried dozens of homes in hilly districts around the city of five million people after monsoon rains lashed the coast at the weekend.

In one incident, a family of five, including three children, were killed when their house was buried under a mudslide.

Mr Rahman says military and civilian rescue teams have been sent to affected areas, while mosques have been asked to house people evacuating their homes.

Communications within the city have been paralysed and telephone links with the rest of the country are down.

Chittagong Mayor Manjurul Alam says one-third of the city is now under about a metre of water, and more than 1.5 million people are affected.

Bangladesh weather department spokesman Sanaul Haq Mandal has also warned that low-lying areas in coastal districts and small islands are likely to be submerged under tidal water.

"We have asked fishing trawlers and boats not to go to deep sea as squally weather and rains will continue for some time," he said.

Officials say flights to the city's Shah Amanat International Airport have been temporarily suspended and Chittagong Seaport, which handles more than 90 per cent of the country's foreign trade, is also closed because of the heavy rains.

Landslides are a regular occurrence in hilly areas of Chittagong.

Experts have previously warned of environmental disasters due to the Government's failure to stop illegal hill cutting, where areas are cleared for housing.

Mr Rahman says the landslides are "very much linked to cutting of hills in this region".

Police chief Moinur Rahman Chowdhury says rescue efforts have been stepped up after rains eased around midday local time on Monday (4:00pm AEST).

"But still our teams could not get to some of the worst affected places," he said.